1. Field of the Invention
Example embodiments of the present invention relate to equalizers and methods of equalizing, and more particularly, to equalizers having a smaller size and/or a wider bandwidth.
2. Description of the Related Art
An equalizer used for continuous-time signal processing simultaneously performs a low pass filtering function and a function of boosting a high-frequency region of an input signal to equalize the input signal. In a DVD or HDD PRML read channel signal process, for example, the equalizer simultaneously carries out an equalizing function of making the pulse shape of a signal input from media stored in a DVD or HDD into a target pulse shape and a filtering function of reducing high-frequency noise input from a pre-amplifier and a VGA.
For processing signals input from high speed disc drive read channels and various media, an equalizer having a wide bandwidth and/or a high boosting gain may be desirable. An equalizer having lower consumption power and/or a smaller circuit area, for example, implemented as a system on chip (SOC) may also be desirable. Thus, it is difficult to design an equalizer having a wider bandwidth.
A wide bandwidth equalizer may use a switched-capacitor (SC) filler or a transconductor-capacitor (Gm-C) filter. A Gm-C filter has an open loop structure and is suitable for a high-frequency operation. A wide bandwidth equalizer may include a circuit for boosting high-frequency components. The −3 dB frequency of a Gm-C filter is determined by a ratio of transconductance (gm) to integrating capacitance (C), that is, gm/C. Thus, to increase the bandwidth of a Gm-C filter, the transconductance gm should be increased and the capacitance C should be decreased. The −3 dB frequency is a factor determining AC response characteristic of the filter and corresponds to a frequency at which the gain of the filter becomes −3 dB.
To increase the bandwidth of a Gm-C filter, an integrating capacitor having a smaller capacitance may be used. The integrating capacitor may be designed by scaling a normalized integrating capacitance determined based on a filter order and a filter type (for example, Bessel, Butterworth, Equiripple filters). The actual capacitance obtained by scaling a normalized capacitance with a desired factor must be larger than a parasitic capacitance. For example, when normalized capacitances of a third-order filter are C1=0.1, C2=0.2 and C3=0.3 and a scale factor is 5 p, the actual capacitances are 0.5 pF, 1.0 pF and 1.5 pF. If a parasitic capacitance, which is added to each integrating node caused by a plurality of transconductors connected in parallel with a circuit for boosting, is 1.0 pF, the scale factor must be larger than 10 p. This is because, when the scale factor is 5 p, there is no problem in the nodes to which C2 and C3 are connected but the capacitance of the node connected to C1, 0.5 pF, is smaller than the parasitic capacitance, 1 pF.
If there is no circuit for boosting connected to the node of C1 but exists only a parasitic capacitance of 0.4 pF caused by a plurality of transconductors, all the capacitances can be scaled even if the scale factor is 5 p when an integrating capacitance of 0.1 pF is added to the node of C1. However, the total capacitance can be increased or decreased according to a boosting algorithm to increase or decrease a chip size.
FIG. 1 is a circuit diagram of a conventional equalizer 100. Referring to FIG. 1, the conventional equalizer 100 is a 7th-order equalizer and includes a lossy integrator 102, three Gm-C biquad circuits 104, 106 and 108, and a boosting circuit 110. The equalizer 100 is of the equiripple type and constructed by adding the boosting circuit 110 to a 7th-order low pass filer.
Each of the three Gm-C biquad circuits 104, 106 and 108 includes a first transconductor 118 connected between an input node 112 and a biquad band pass node 114, a first capacitor 120 connected between the biquad band pass node 114 and a ground voltage, a second transconductor 122 connected between the biquad band pass node 114 and a biquad low pass node 116, a third transconductor 124 that is connected between the biquad band pass node 114 and the biquad low pass node 116 and forms a feedback loop with the second transconductor 122, a fourth transconductor 126 connected to the biquad low pass node 116 in a self-feedback configuration, and a second capacitor 128 connected between the biquad low pass node 116 and the ground voltage.
A biquad circuit is a second-order filter and may be composed of operational amplifiers or transconductors as shown in FIG. 1. When a plurality of biquad circuits are serially connected, a filter having a more than fourth order can be obtained.
The boosting circuit 110 boosts a high-frequency region of the equalizer and includes an inverting transconductor 130 connected between the input node of the first Gm-C biquad circuit 104 and the input node of the second Gm-C biquad circuit 106, and a non-inverting transconductor 132 connected between the input node of the second Gm-C biquad circuit 106 and the input node of the third Gm-C biquad circuit 108. A non-inverting transconductor has input and output signals having the same phase and an inverting transconductor has input and output signals having a phase difference of 180°.
The normalized capacitances of the 7th-order equiripple filter of FIG. 1 are represented in Table 1.
TABLE 1CapacitorNormalized capacitanceC11.1610C21.2795C30.5938C40.5224C50.6485C60.2133C70.8729
In the structure of the equalizer 100 shown in FIG. 1, the outputs of the transconductors 130 and 132 for boosting are connected to integrating nodes of capacitors C3 and C5, that is, the biquad low pass node of the first biquad circuit 104 and the biquad low pass node of the second biquad circuit 106. Accordingly, parasitic capacitances generated from the outputs of the transconductors 130 and 132 are added to the integrating nodes connected to the capacitors C3 and C5, and thus parasitic capacitances of the integrating nodes of the capacitors C3 and C5 are larger than parasitic capacitances of capacitors C1, C2, C4 and C6. Referring to Table 1, the equalizer 100 is not efficient with respect to capacitor sizes because the normalized capacitances of the capacitors C3 and C5 are smaller than the normalized capacitance of the capacitor C1 or C2. That is, a large parasitic capacitance is added to a node having a small normalized capacitance to increase a scale factor for making the actual total capacitance, and thus other integrating capacitances should be scaled with a large scale factor.
To produce a high-frequency filter using identical transconductors, the total capacitance of each integrating node must be small. The total capacitance of one integrating node is represented by Ctot=Cnor×Sf=Sint×Cpar, where Ctot denotes the total capacitance, Cnor denotes a normalized capacitance, Sf is a scale factor, Sint is an integrating capacitance connected to a circuit, and Spar is a parasitic capacitance added to the circuit.
An Nth-order filter has N integrating nodes, N integrating capacitances, N normalized capacitances, N parasitic capacitances and one scale factor. If the parasitic capacitance Cpar is 0 at each node, Cnor×Sf=Cint. However, Cint=Cnor×Sf-Cpar because the parasitic capacitance Cpar is not zero in the actual circuit.
For example, when Cnor2=1.2795, Cnor3=0.5938, Sf=3 p and Cpar=0 in a seventh-order filter, Ctot2=3.8385 pF and Ctot3=1.7814 pF. When Cpar2=2 pF and Cpar3=1.5 pF, Cint2=1.8385 pF and Cint3=0.2814 pF. When Cpar2=2 pF and Cpar3=2.5 pF, however, the second node is normally scaled but the third node is not properly scaled because Ctot3 is smaller than Cpar3. The scale factor Sf must be increased and thus all the seven integrating capacitances are increased. This increases circuit size.
In the equalizer 100 of FIG. 1, a boosting gain K is determined by a ratio of transconductance gmk of transconductors added to the equalizer 100 for generating zero to transconductance gm of transconductors used to constitute the filter. That is, K∝gmk/gm. Accordingly, when a large-size transconductor is used to constitute a high-frequency filter, gm is increased and thus transconductors for boosting should be increased in the same ratio to obtain a specific boosting gain K. Furthermore, the sizes of transconductors added to the filter should be further increased in order to raise the boosting gain K.
Accordingly, conventional equalizers may have a problem that its size is increased in order to increase its bandwidth, obtain a specific boosting gain at a high frequency and/or raise the boosting gain. That is, when transconductance is increased to widen the bandwidth of a Gm-C filter in a conventional equalizer, the total capacitance is increased and thus the bandwidth cannot be widened. When capacitances are reduced, integrating capacitances may become smaller than parasitic capacitance. When the integrating capacitances and transconductance are increased, chip size is increased. Furthermore, when a boosting gain is raised using the conventional equalizer, sizes of transconductors should be increased to result in an increase in the chip size.